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2D massless QED Hall half-integer conductivity and graphene. (English) Zbl 1231.81095

Summary: Starting from the photon self-energy tensor in a magnetized medium, the 3D complete antisymmetric form of the conductivity tensor is found in the static limit of a fermion system \(C\)-non-invariant under fermion-antifermion exchange. The massless relativistic 2D fermion limit in QED is derived by using the compactification along the dimension parallel to the magnetic field. In the static limit and at zero temperature, the main features of the quantum Hall effect (QHE) are obtained: the half-integer QHE and the minimum value proportional to \(e^{2}/h\) for the Hall conductivity. For typical values of graphene the plateaus of the Hall conductivity are also reproduced.

MSC:

81V70 Many-body theory; quantum Hall effect
81V80 Quantum optics
82D80 Statistical mechanics of nanostructures and nanoparticles
81V10 Electromagnetic interaction; quantum electrodynamics
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